Atmospheric-TurbulenceCompensation ExperimentsUsing Cooperative BeaconsDaniel V. Murphy

III Lincoln Laboratory recently completed the three-year Short-WavelengthAdaptive Techniques (SWAT) field program, designed to investigate theperformance of adaptive optics in a variety of scenarios. This article describesthe operation of the SWAT adaptive optics system working with cooperativebeacons. Examples are presented of system operation in compensating starimages and in propagating a compensated laser beam to a satellite.

ADAPTIVE OPTICS makes it possible to seethrough the atmosphere without sufferingthe resolution degradation caused by turbu­

lence. Applications include the high-resolution view­ing of exoatmospheric objects and the propagation ofnear-diffraction-limited laser beams to space. Astro­nomical objects and satellites are of obvious interestfor high-resolution imaging. Potential applications forlaser propagation include ground-to-space communi­cations and the transmission of high-energy lasers tointercept ballistic missiles.

Adaptive optics systems require a reference lightsource, or beacon, to measure the turbulence-inducedatmospheric aberrations. The most convenient ar­rangement is for the beacon to be located at the objectof interest and shining down toward the adaptiveoptics system. In such cases the beacon is said to becooperative. Cooperative beacons can be either man­made (e.g., a light source on a satellite) or natural(e.g., a star). Scenarios that do not provide for abeacon at the target are termed uncooperative; specialtechniques are required for using adaptive optics insuch cases (see the article by Byron G. Zollars [1] inthis issue).

This article describes the operation of the Short­Wavelength Adaptive Techniques (SWAT) systemworking with cooperative beacons. The SWAT sys­tem was installed in a beam director that has a 60-cm

aperture at the Air Force Maui Optical Station(AMOS) facility on the island of Maui, Hawaii. Lo­cated at an elevation of 10,000 ft at the top of thedormant volcano Haleakala (Figure 1), the site hasthe advantages of fairly low turbulence, good atmo­spheric transmission, and generally dear skies. TheSWAT system was used to compensate the imagesof bright stars as well as to transmit a low-power,compensated laser beam to a satellite. Lincoln Labo­ratory conducted tests from May 1988 to mid-April1991.

Adaptive Optics System forStar Compensation

Compensation of star images to enhance astronomi­cal observations was one of the first recognized appli­cations for adaptive optics. A recent review of thefield is provided in Reference 2. Although the SWATsystem was configured on Maui for propagating abeam to a satellite rather than for astronomical ob­servations, good compensated imaging could stillbe achieved by using some of the brightest stars asbeacons.

The operation ofan adaptive optics system in com­pensating the image of a star is illustrated schemati­cally in Figure 2. In this configuration, the star itselfserves as the beacon for the adaptive optics. Starlightis collected by the beam director (comprising a track-

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FIGURE 1. Air Force Maui Optical Station (AMOS) and the University of Hawaii facilitieslocated at the edge of the Mount Haleakala crater on Maui, Hawaii. AMOS is the largewhite complex on the left.

ing flat and telescope), is reflected off the fast-steer­ing mirror and the deformable mirror, and is sensedboth by the wavefront sensor and by a far-field cam­era that records the image. When the adaptive op­tics system does not apply any correction, the wave­front aberration imposed on the starlight by itspassage through the atmosphere results in a jitter­ing, distorted image in the camera. When thesystem does apply a correction, the conjugate ofthe aberration that the wavefront sensor measuresis applied to the deformable and fast-steering mir­rors so that the wavefront is flat after reflectingoff the deformable-mirror surface. The far-fieldcamera then sees a jitter-free, unaberrated image ofthe star.

The deformable mirror does not usually performcompensation of the tilt component of turbulence.As shown in Figure 2, the task is off-loaded to aseparate fast-steering mirror to reduce the stroke re­quirement for the deformable mirror. In this con­figuration, the deformable mirror compensates onlythe tilt-removed phase, often referred to as thewavefront figure. Commands for the fast-steeringmirror can be obtained either from the phase that the

26 THE LINCOLN LABORATORY JOURNAL VOLUME 5, NUMBER I, 1992

wavefront sensor measures or from a separate sensorthat measures only the overall wavefront tilt. TheSWAT system utilizes a separate tracker so that tiltcompensation (i.e., tracking) can be performed evenwhen the wavefront sensor is not operating.

Deformable Mirror

The deformable mirror is the active wavefront correc­tor, and its characteristics largely determine the capa­bility ofthe entire adaptive optics system. The impor­tant characteristics of a deformable mirror are theactuator density, influence function, stroke, and re­sponse speed. The actuator density is perhaps thedominant characteristic because it determines the high­est spatial frequency of the aberration that thedeformable mirror can compensate. The influencefunction-the shape of the mirror surface in the vi­cinity ofan extended or retracted actuator-also playsa role in defining the spatial spectrum of the correc­tion. The stroke of the mirror is the peak-to-peakdisplacement that an actuator can achieve. The strokemust be sufficient to apply corrections fully, bothfor turbulence and for static aberrations in the op­tics. Finally, the deformable mirror along with its

-MURPHYAtmospheric-Turbulence Compensation Experiments Using Cooperative Beacons

TrackingFlat

60-cm LaserBeam Director

Fast-Steering~+- ~,

Mirror

DeformableMirror

241Voltages

Deformable-MirrorDrivers

, .

241Phases

Tracker

~-;;s:ta:r~1m:a~g::e:::r--il:====::;It;rIBeamSp litter

DigitalWavefront

Reconstructor

218x

218

Gradients

PulsedWavefront

Sensor

FIGURE 2. The Short-Wavelength Adaptive Techniques (SWAT) system performing co­operative-mode compensation of a star. In the cooperative mode, the beacon is located at theobject of interest.

electronic drivers must be fast enough to keep upwith the changing atmospheric turbulence; this re­sponse time requirement typically is on the order ofmilliseconds.

The SWAT deformable mirror, built by LittonItek Optical Systems, uses low-voltage electrostrictiveactuators that push and pull against a thin, reflectivefacesheet (Figure 3). The mirror has 241 actuators ina 17 X 17 rectilinear array with the corners cut off.The actuator spacing is 7 mm at the mirror, which isequivalent to 3.3 cm in the atmosphere after magni­fication in the telescope portion of the beam director.The 3.3-cm actuator spacing is appropriate for near­diffraction-limited compensation of turbulence asstrong as ro = 5 cm, where ro is the atmosphericcoherence diameter (see the box "Derivation ofTur­bulence-Imposed Requirements for Adaptive OpticsComponents"). For an applied voltage of 300 V, themirror has a maximum stroke of 3.5 11m, which ismore than ample to correct turbulence and opticsaberrations. The rise time of the electronic drivers

and the mechanical resonances in the mirror struc­ture itself determine the temporal characteristics ofthe deformable mirror. The SWAT deformable mir­ror is able to settle to a desired wavefront figurewithin a few hundred microseconds of a command.Figure 4 shows the mirror drive electronics.

Wavefront Sensor

It is difficult to build a sensor to measure the wavefrontphase directly, so almost all sensors measure the localgradients of the wavefront in an array that is matchedto the deformable-mirror actuators, as shown in Fig­ure 5. Values of the phase at each actuator locationare then obtained by calculating the phase from thegradients in a separate wavefront reconstructor.

The SWAT wavefront sensor (WFS) is based onthe classic Hartmann test for examining optics. Asshown in Figure 6, the sensor uses an array of lensletsto divide the incoming wavefront into subapertures,with the light in each subaperture brought to focuswithin a 4 X 4 subarray of pixels on a charge-coupled

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DERIVATION OF TURBULENCE-IMPOSEDREQUIREMENTS FOR ADAPTIVE OPTICS

COMPONENTS

THE ESSENTIAL REQUIREMENTS foran adaptive optics system can bederived from the theoretical prop­erties ofturbulence-induced wave­front aberrations. As the follow­ing paragraphs show, expressionsfor quantities such as deformable­mirror and tilt-mirror strokes andwavefront-sensor measurementrange have simple forms that in-

)5/3 hvolve the term (D/ro ,wereD is an aperture diameter (eitherthe whole aperture or a subaper­ture) and ro is the atmosphericcoherence diameter [1]. Theparameter ro is a measure ofthe effect of turbulence on awavefront; it is obtained by inte­grating the turbulence strengthC; over the line of sight throughthe atmosphere:

L

ro-5/3 = 0.423k2JC;(z)dz,

o

where k is the wave number oflight (equal to 2n/l..) and L is thedistance from the receiver to thelight source (the top of the atmo­sphere for a star). C;(z), knownas the refractive-index structurefunction, is a measure of the tur­bulence strength and is strongly

dependent on altitude and localterrain. The parameter ro hasproven to be very useful becauseit has a simple physical interpre­tation: the resolution along a pathcharacterized by ro is limited byturbulence to approximately theresolution that would be obtainedby a diffraction-limited apertureof diameter roo Values of ro forvisible light vary from about 20cm at good astronomical sites toless than 5 cm. Thus, even thoughlarge ground-based telescopeswith diameters up to 4 m cangather a lot of light, they canachieve no better resolution thantelescopes with diameters ofa fewtens of centimeters.

In this article, wavefront aber­rations are expressed in units ofwavelengths of light for visiblelight (I.. = 0.5 pm). This conven­tion is ofren a point of confusionbecause turbulence-induced aber­rations are, to the first order, in­dependent ofwavelength. Turbu­lence creates variations in theoptical path that are character­ized in units of length, indepen­dent of the color of the light thatpasses through the atmosphere.The effect on the image, howev-

er, does depend on the wave­length. For example, turbu­lence may cause the optical-pathlengths of two nearby rays todiffer by 1 pm. For visible light(I.. = 0.5 J1ffi) this difference rep­resents a 2-wave aberration andwill severely degrade an image.But for light at 10 pm, the differ­ence represents an aberration ofonly 0.1 wave and will barely de­grade an image at all. Thus theuse ofwavelength as a unit is con­venient because it provides a sub­jective feel for the importance ofthe aberration at the wavelengthof interest.

Deformable Mirror

The difference between a turbu­lence-induced wavefront aberra­tion and the best correction thatcan be applied by a deformablemirror with an array of discreteactuators is known as the fittingerror. The spatial variance of thefitting error [2] is given simplyby

where dis the inter-actuator spac-

.f

device (CCO) detector. When the CCO is read out,the pixels from each subarray are processed with acentroid algorithm to determine the location of thefocal spot. The displacement of the spot from the

28 THE LINCOLN LABORATORY JOURNAL VOLUME 5. NUMBER 1. 1992

center of the subarray is proportional to the averagetilt, or gradient, of the portion of the wavefront inthat subaperture.

It is worth emphasizing that the wavefront-sensor

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..

ing and J1 is a constant that de­pends on the influence functionof the mirror. For the SWAT sys­tem, d = 3.3 cm (17 actuatorsacross a diameter of 56 cm) andJ1 = 8.7 X 10-3 waves2. In a sys­tem intended to approach dif­fraction-limited compensation, itis generally desirable to haveGf $; lIS wave rms. Equation ApredictS, then, that the SWAT sys­tem should be capable ofcorrect­ing turbulence with a strength cor­responding to ro ::::: 5 cm.

The stroke of a deformablemirror must be at least largeenough to apply a correction equalto the peak-to-peak wavefront ab­erration. The variance of the un­compensated wavefront figure[3] is

( )

S/32 -3 D 2

GI/l =3.57 x 10 ro waves,

where D is the overall diameter ofthe telescope aperture. As an ap­proximate rule of thumb, thepeak-to-peak phase aberration isabout 5 times Gifi' or about 2.2waves for ro = 5 cm. The strokerequired to apply a I-wave aber­ration is only 0.25 J1m because 1wave is 0.5 J1ffi and the wavefrontaberration resulting from reflec­tion is twice the aberration of thesurface of the mirror. Thus a

Stroke ofonly 0.55 J1ffi is requiredto compensate turbulence ofstrength ro =5 cm.

Wavefront Sensor

The strength of the turbulenceand the size of a subapertutedetermine the required gradi­ent measurement range of thewavefront sensor. The varianceof the wavefront gradients causedby turbulence and measuredwithin a subaperture of diameterdis

G~= 0.170(: )S/~waves/sub- 2o aperture) .

Again, with the rule of thumbthat the extreme range of gradi­ents is about five times the stan­dard deviation, the required dy­namic range for turbulence ofStrength ro = 5 cm is ± 0.75 waves/subaperture.

Fast-Steering Mirror

The required angular range ofthe fast-steering mirror can beestimated from the turbulence­induced tilt variance [3] gIven

by S/3

a~ =0184(~)

-(~r(radians of tilt)2 .

For ro = 5 cm, the maximumwavefront tilt is ±7 J1rad, whichrequires a mechanical mirror tiltof±3.5 j1fad. The mechanical-tiltrequirement is actually ±3.5 j1fadx 14.1 ::::: ±50 j1fad, where 14.1 isthe magnification between thefast-steering mirror (beam diam­eter = 4.0 cm) and the 56-cmbeam in the atmosphere.

It is easy to see why tilt is usu­ally unloaded from the deform­able mirror to a separate correc­tor. Driving a deformable mirrorto a tilt of 3.5 J1rad would re­quire a peak-to-peak stroke of3.5 j1fad x D ::::: 2 J1ffi. This re­quirement is larger than thestroke required to compensatethe higher-order wavefront-figureaberration, and is uncomfortablyclose to the maximum strokecapability of the SWAT deform­able mirror.

References1. D.L. Fried, "Limiting Resolution look­

ing Down through the Aonosphere," j.Opt. Soc. Am. 56,1380 (1966).

2. D.P. Greenwood, "Mutual CoherenceFunction ofa Wave Front Corrected byZonal Adaptive Optics," j. Opt. Soc.Am. 69, 549 (1979).

3. D.P. Greenwood and D.L. Fried, "Pow­er Specrra Requirements for Wave­Front-Compensation Systems," j. Opt.Soc. Am. 66, 193 (1976).

measurements are independent ofwavelength; in fact,the WFS works well with white light. The displace­ment of a focal spot at the detector plane is propor­tional to the average tilt of the portion ofthe wavefrontwithin that subaperture-independent ofwavelength.Thus the WFS actually measures an array of geomet-

ric wavefront tilts. For convenience, these tilts (orgradients) are usually expressed in units of opticalpath difference in wavelengths of light (J. = 0.5 J1m)

across a subaperture.An important characteristic of a WFS is the mag­

nitude of the largest gradient that can be measured. In

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the SWAT system, the maximum gradient is limitedby the size of the 4 x 4 subarray corresponding toeach subaperture. If a focal spot moves too far offcenter, energy from the spot will spill into the adja­cent subaperture and compromise the measurementsin both subapertures. The SWAT WFS has a linearmeasurement range of ±1.4 waves/subaperture,sufficient to measure turbulence and static-opticsaberrations (see the box "Derivation of Turbu­lence-Imposed Requirements for Adaptive OpticsComponents").

Another critical characteristic for a WFS that workswith low signal levels is the sensor's photon sensitivity,characterized by the measurement error as a functionof light level. The variance of the gradient error for aHartmann sensor with a 4-pixel centroid algorithm is

2 0.526 6.09(,-2 2<Tg =-- + ; (waves/subaperture), (1)

1]N (1]N)

where N is the number of photons arriving at thedetector per measurement interval per subaperture, 1]

is the detector quantum efficiency, and <Te is the read­out noise of the detector in electrons. The first termin Equation 1 is the photon shot noise, which isderived from the arrival statistics of the photons, andthe second term is the noise that the detector im-

Pusher

ActuatorStack

ElectricalLeads

(a)

poses. Ideally, the overall noise would be determinedby photon statistics, but in practice the detector noisedominates the low-light performance of the SWATsensor.

The SWAT WFS utilizes 64 x 64, backside-illumi­nated CCD detectors developed at Lincoln Labora­tory [3]. The detectors have an average quantumefficiency of about 80% over the wavelength band of0.42 to 0.54 J.lIIl transmitted by the optics, and thenoise of the chips and readout electronics combinedis 25 to 30 electrons per pixel at a readout rate of 4.2Mpixels/sec. From Equation 1, these numbers predictthat a single-measurement root-mean-square (rms)gradient noise of /5 wave/subaperture can be achievedwith N :::: 1350 photons. This photon flux corre­sponds rougWy to the signal received from a brightstar of visual magnitude zero with the WFS runningat a 2-kHz frame rate.

In addition to the optics and detectors describedabove, the WFS has processing electronics for per­forming the centroid calculation and for applying theappropriate calibration factors to convert the raw cam­era data to gradients. The time required to frame, orcycle, the cameras and output the entire serial streamof gradients is approximately 225 tlSec.

A thorough description of the design and per­formance of the SWAT WFS can be found in the

(b)

FIGURE 3. Deformable mirror: (a) schematic representation of a continuous-facesheet deformable mirror, and (b)photograph of the SWAT deformable mirror.

30 THE LINCOLN LABORATORY JOURNAl VOLUME 5. NUMBER 1, 1992

..

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FIGURE 4. SWAT control electronics for adaptive optics. From right to left, the rackscontain (1) driver electronics for the deformable mirror, (2) a wavefront reconstructor(bottom) and a real-time display for wavefront-sensor data (top). (3) electronics for dataformatting and overall system control, and (4) a video display for the charge-coupleddevice (CCD) far-field camera.

solved to find the best estimate of the phase in theleast-squares sense [5]-the solution has the simpleform

where ~ is an estimate of the phase and B is a241 X 436-element reconstruction matrix. Thus thereconstruction of the phase from the gradientmeasurements can be performed as a single matrix­multiplication operation.

The matrix multiplication is straightforward toimplement, but high data rates are required to keepup with the maximum frame rate of the wavefrontsensor. The phase reconstruction was performed inthe SWAT system by a special-purpose_digital proces­sor [6] designed and built at Lincoln Laboratory (Fig­ure 4). The processor has 241 parallel channels thatcorrespond to the 241 phase nodes. Each channeluses commercially available multiplier/accumulator

article by Herbert T. Barclay et al. [4] lfi thisIssue.

Reconstructor

A gradient measured in the array shown in Figure 5can be approximated as the difference of thephase values at the two nodes it connects. In thatcase, the wavefront measurement can be modeled asthe matrix operation

(2)

where g is a 436-element vector comprising the mea­sured gradients (there are 218x and 218y gradients),A is a 436 X 241-element differentiation matrix, ; is a

241-element vector of the values of the wavefrontphase at the actuator locations, and n is a vectorrepresenting the gradient measurement noise. Al­though Equation 2 cannot be solved uniquely for thephase because of the noise term, the equation can be

~ = Bg, (3)

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x-Su bapertu re! ~. .

. ~. ~. ~. ~. ~.

--. x-Gradient

• y-Gradient

• Actuator

FIGURE 5. Layout of the x- and y-gradients measured bythe wavefront sensor. Each gradient is averaged over asquare subaperture. Separate detectors are used for thex- and y-gradients to permit the spatial offsetting of thex- and y-subapertures, as shown.

chips to calculate a weighted, linear sum of all inputgradients, in which the weights are just the matrixelements from Equation 3:

~n =L Bn,igi .

As the gradient values are clocked into the reconstruc­tor, each value is multiplied by the appropriate matrixelement read from memory and the value is thenadded to the cumulative sum. The reconstruction iscomplete on receipt of the last gradient from thewavefront sensor, so the pipeline delay is only a fewcycles of the 5-MHz clock. Several different re­construction matrices can be stored in memory atone time, allowing easy switching from, for ex­ample, reconstruction of the full phase to recon­struction of the wavefront figure.

Tracking System

The tracking system compensates tilt fluctuations in-

32 THE LINCOLN LABORATORY JOURNAl VOLUME 5. NUMBER 1, 1992

duced by turbulence as well as by mechanical vibra­tions in the optical train. The essential components ofthe system are a tilt sensor, control electronics, and afast-steering mirror. The principal characteristics arethe angular range of the fast-steering mirror and thetemporal response of the system.

The SWAT tilt sensor is a position-sensing photo­multiplier tube (PMT) manufactured by HamamatsuCorp. The sensor uses a 12 x 12 grid of anode wiresto resolve the position of a spot of light that is inci­dent on the photocathode. When the PMT is used asa tracker, the spot is formed by focusing the beaconlight onto the face of the tube. In effect, the PMTmeasures overall tilt much as a subaperture in thewavefront sensor measures the local wavefront gradi­ent, but with a much wider measurement range be­cause of the 12 anode wires. Depending on the con­figuration of the optics, the tracker field of view canbe as large as 150 .urad.

The SWAT fast-steering mirror, designed and builtat Lincoln Laboratory, uses three piewelectric actua­tors to provide two-axis tilt for a 2.5-inch mirror. Themaximum angular range of the mirror is BOO .urad,which corresponds to a range of ±20 .urad in theatmosphere after magnification in the optics. Thisrange is well in excess of the B.5 .urad required forturbulence compensation, as derived in the box "Deri­vation of Turbulence-Imposed Requirements forAdaptive Optics Components." The extra range isused to compensate mechanical vibrations and to pullin targets that are slightly off boresight.

The tracking system can be operated with a closed­loop bandwidth of either 225 or 600 Hz. The lowerbandwidth is generally adequate for tracking stars;the higher bandwidth was provided for trackingsatellites.

Closed-Loop Operation ofSystem

When a continuous beacon source is available, theadaptive optics system can be operated in the closed­loop mode. Tilt compensation is performed by sim­ply closing the tracking servo loops. Wavefront-figurecompensation is performed by repetitively framingthe wavefront sensor at a high rate to provide valuesof the phase at the 241 actuator locations ofthe deformable mirror. The figure compensation is

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ith Subaperture(4-4)

\..

IncomingWavefront

•••

•• Array of Lenslets• in Entrance Pupil

/

• • •

2-D Detector Arrayin Focal Plane

/

To Processorand DigitalReco nstructor

(0,0)

FIGURE 6. Principle of operation of a Hartmann wavefront sensor. The local phase gradient at the ithsubaperture is proportional to !!.xi. The digital reconstructor computes the phase from the measuredgradients.

applied by driving each actuator of the deformablemirror with its own servo loop to null the phasecorresponding to that location. When the 241parallel servo loops are closed, the deformable mirroris driven continuously to assume whatever shape isrequired to flatten the phase that the wavefront sensormeasures. A servo bandwidth on the order of 100 to

200 Hz is required for the system to keep up withthe changing atmospheric distortion when compen­sating a star.

Compensating the image ofa bright star provides agood demonstration of the operation of the entiresystem. The performance of the tilt-compensationsystem is summarized in Figure 7, which shows thepower spectral density of the single-axis tilt fluctua­tions that were measured by using a star as a beacon.The open-loop spectrum shows the turbulence­induced tilt disturbance in addition to a number ofdiscrete lines caused by mechanical vibrations in thebeam director. The closed-loop spectrum shows theresidual error comprising both uncompensated tilt

and sensor measurement noise. In closed-loop opera­tion, the cumulative rms jitter out to the servo band­width of 600 Hz was less than 50 mad, which corre­sponds to a residual rms image jitter of about 2

10 th

the diffraction-limited spot size for visible light. Thehigh bandwidth and low residual jitter achieved bythe tracking system ensured that there was essentiallyno tilt-induced smearing of the star image.

The system's figure-compensation capability is dem­onstrated in Figure 8, which shows compensatedand uncompensated images of the star Sirius (visualmagnitude -1.6) at an elevation of 51°. The imageswere recorded by a 64 X 64 CCD camera that wassimilar to the ones used in the wavefront sensor;the angular field of view of the camera was 19 ,urad.Coatings on the optical components limited the wave­length passband to 0.42-0.54 ,um. Because bothimages were recorded with the tracking loops closed,the degradation of the uncompensated image wascaused entirely by aberrations in the atmosphere andsystem optics.

VOLUME 5. NUMBER 1. 1992 THE LINCOLN LABORATORY JOURNAL 33

1000

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10 100Frequency (Hz)

FIGURE 7. Power spectral densities (PSD) of single-axis tilt fluctua­tions measured from the star Sirius with the tilt servo loops open andclosed. The cumulative jitter out to the 6OO-Hz servo bandwidth was6 wad root mean square (rms) in open-loop operation, and 43 nradrms in closed-loop operation.

The image of a point source can be characterizedquantitatively by the StreW ratio-the ratio of thepeak intensity of the image to the peak intensity of adiffraction-limited image. The Strehl ratio can be

easily calculated from a compensated image if oneassumes that the exposure contains all the energy of adiffraction-limited image, a reasonable assumption atleast for compensated images. For the compensated

FIGURE 8. Images of the star Sirius with the figure-compensation loops (a) open and (b) closed. Thetracking loops were closed for both images, and each image is the average of 50 exposures recordedover a 1-sec interval. The star elevation was 51°, and '0 (see the box "Derivation of Turbulence-ImposedRequirements for Adaptive Optics Components") was approximately 9 em. The Strehl ratio was about0.03 for the image in part a and about 0.3 for the image in part b. (The Strehl ratio is the ratio of the peakintensity of the image to the peak intensity of a diffraction-limited image.)

34 THE LINCOLN LABORATORY JOURNAl VOLUME 5. NUMBER 1, 1992

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(a) (b)

FIGURE 9. The binary star Castor: (a) uncompensated and (b) compensated images. The tilt and figureloops were both open for the uncompensated image and closed for the compensated image. Theseparation between the two stars is 15 .urad (approximately 3.1 arc sec).

, .

image in Figure 8, the Strehl ratio is 0.3; for theuncompensated image it is about 0.03. The principalfactors that limit the compensated Strehl ratio are thefitting error (see the box "Derivation of Turbulence­Imposed Requirements for Adaptive Optics Compo­nents"), wavefront-sensor measurement noise, andresidual phase fluctuations outside the correction band­width.

Figure 9 shows another compensated image, thatof Castor-a binary star of visual magnitude 2.0 forwhich the separation of the two components is 15,urad (3.1 arc sec). An image with no compensation(Figure 9[a]), and one with tilt and figure compen­sation (Figure 9[b]) are shown; each image is theaverage of 50 frames collected over a I-sec interval.Because Castor is much dimmer than Sirius, thecompensation is nowhere near the diffractionlimit. Nevertheless, the system easily resolved the twostars, which were clearly not resolved without anycorrection.

Scoring-Beam Compensation

As mentioned earlier, the SWAT system was primarilydesigned to compensate an outgoing, low-power laserbeam. This type ofcompensation can be accomplished

by bringing the laser beam, referred to as the scoringbeam, into the optical path so that it reflects off thedeformable and fast-steering mirrors on its waythrough the system and out the beam director. Com­pensation of the scoring beam works in the same wayas compensation of a beacon image except that thecorrection is applied to the scoring beam before itencounters the atmospheric aberration rather thanafter. The precorrection applied to the scoring beamis exactly canceled by the aberrations experienced bythe beam as it propagates through the atmosphere.Consequently, the scoring beam has a flat wavefrontat the top of the atmosphere and continues on to thetarget as a diffraction-limited beam.

The effectiveness of scoring-beam compensation isbest judged by examining the intensity profile of thebeam in the far field. A convenient way to make suchmeasurements was provided at the AMOS site bya trailer located about 150 m away from thebeam director

1(Figure 10). The trailer was equipped

with both a laser source to serve as the beacon and a100 X 100-pixel solid state camera to record the im­age of the focused scoring-laser spot. Although propa­gation over a short horizontal path does not modelall aspects of ground-to-space propagation, the setup

VOLUME 5, NUMBER 1,1992 THE LINCOLN LABORATORY JOURNAL 35

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FIGURE 10. Site of the horizontal-path measurements at AMOS. The red line indicatesthe 146-m propagation path from the small dome that houses the laser beam director tothe instrumented target trailer.

was a good test of system operation because the inte­grated turbulence strength over the I50-m path tothe trailer was comparable to that for a vertical pathto space.

In the horizontal-path tests, the beam director waspointed at the trailer and the trailer beacon was ac­quired in the wavefront sensor and far-field CCOcamera. The scoring beam was then transmitted outof the beam director and detected by the trailer's solidstate camera. Closing the adaptive optics loops (bothtilt and figure) resulted in the simultaneous compen­sation of the beacon image and laser spot. Because thescoring-laser beam and beacon light traversed the samepath through the turbulence, they experienced thesame degree of correction by the adaptive optics, andthey generally had similar Strehl ratios. Nevertheless,the compensated beacon image and scoring-laser spotwere not identical. The theoretical diffraction-limitedprofiles for the two were different because the laserbeam and beacon light had different near-field inten­sity profiles: the scoring beam had a Gaussian profilewith a 11e2 diameter of 48 em while light from thebeacon uniformly filled the 56-em aperture. In addi­tion, instrumental artifacts in the imaging system

36 THE LINCOLN LABORATORY JOURNAL VOLUME 5. NUMBER 1, 1992

broadened the beacon image slightly.An example of good compensation over the path

to the target trailer is illustrated in Figure 11, whichshows compensated images of the beacon and of thescoring-beam spot recorded simultaneously over aI-sec interval. As expected, the calculated Strehl ratiosfor the two images are comparable. Figure 12 charac­terizes the two compensated images as well as a pairof uncompensated images that were recorded withthe deformable-mirror loops open but the trackingloops still closed. These figures, known as power-in­bucket plots, show the total power that would becollected within a circular "bucket" of a given radiuscentered on the image. It is easy to see qualitativelythat the adaptive optics system dramatically de­creased the spread of energy in both the beaconimage and at the focus of the scoring laser. The ex­pected difference in the shapes of the two images isreadily apparent in the diffraction-limited and com­pensated curves.

Propagation to a Satellite

One of the principal goals of the SWAT program wasto propagate a compensated laser beam to a low-

. .

-MURPHYAtmospheric-Turbulence Compemation Experiments Using Cooperative Beacom

(a) (b)

FIGURE 11. Compensated profiles of the (a) scoring beam and (b) beacon image recorded simultaneouslyfor propagation over a horizontal path. Each profile has been averaged over 1 sec. The value of,o was about5 em and the Strehl ratio for both images was about 0.5.

earth-orbiting satellite. Ground-to-space propagationof a compensated scoring beam was first demon­strated in 1985 as part of Lincoln Laboratory's Atmo­spheric-Compensation Experiment (ACE), but theslew rate of a low-orbit satellite is significantly higherthan that of the sounding rockets used as targets inthe ACE program. Propagation to a satellite, there-

0.8

....Q)

3:0 0.6Cl.

<:JQ)

~0.4u

c:W

. 0.2.

Bucket Radius (wad)

(a)

fore, placed a greater burden on the adaptive opticsbecause it demanded a faster temporal response.

The setup for transmitting a scoring beam to asatellite (Figure 13) was similar to that used for starcompensation except for the addition of the instru­mented satellite and a visible laser beam (in additionto the scoring beam) to illuminate a retroreflector

Bucket Radius (wad)

(b)

FIGURE 12. Power-in-bucket curves for the compensated profiles from Figure 11, the corresponding uncompensatedprofiles, and the theoretical diffraction-limited profiles for the (a) scoring beam and (b) beacon image. The curves showthe total power that would be collected within a circular "bucket" of a given radius centered on the image.

VOLUME 5. NUMBER 1.1992 THE LINCOLN LABORATORY JOURNAl 37

-MURPHYAtmospheric-Turbulence Compensation Experiments Using Cooperative Beacom

beacon on the satellite. The experiment was performedby first acquiring the satellite on the boresight of thebeam director, and then transmitting the beam fromthe retro-illuminating laser to irradiate the retro­reflector on the satellite. The laser light reflected fromthe retroreflector served as the beacon for the trackingsystem and for the adaptive optics. Closing the track­ing and deformable-mirror servo loops resulted in acompensated image of the beacon in the far-fieldCCD imager. At the same time, closing the loops alsoresulted in compensation of the outgoing scoringbeam, which could then propagate to the satellite as a

near-difFraction-limited beam. A detector array onthe satellite was used to measure the profile of thescoring beam in order to characterize the degree ofthe compensation. The data from the satellite weretelemetered to the ground and made available fordisplay in real time.

The target satellite used for the ground-to-spacephase of the SWAT program was designed and builtspecifically by the Naval Research Laboratory to mea­sure the intensity profiles ofground-based laser beams.The satellite, known as the Low-Power Atmospheric­Compensation Experiment (LACE), was launched

Detector Array (85 Photodetectors)

..

241Phases

2Tilts

241Phases

Retro refl ecto rIlluminating

Laser

Precision Tracker

CCD Imager

PointingMirror SWAT

Receiver

1550 km

Naval ResearchLaboratory

Trailer•

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DigitalWavefront

Reconstructor

218x

218y

Gradients

WavefrontSensor

FIGURE 13. The SWAT adaptive optics system propagating a laser beam to the Low-Power Atmospheric­Compensation Experiment (LACE) satellite. Equipment specific to the satellite experiment were the satelliteitself, the receiver for the telemetered data, and the retro-illuminating laser.

38 THE LINCOLN LABORATORY JOURNAl VOLUME 5, NUMBER 1, 1992

-MURPHYAtmospheric-Turbulence Compensation Experiments Using Cooperative Beacons

(a) (b)

FIGURE 14. The detector array on the LACE satellite: (a) photograph and (b) diagram.

, ,

into a 547-km circular orbit with a 43° inclination inFebruary 1990. (Note: A 0° orbit circles the equator;an orbit with a 90° inclination goes over the poles.)The features of the satellite most important for adap­tive optics experiments were the retroreflector beaconand the detector array.

The LACE satellite used a retroreflector as a bea­con to avoid the large power load that would havebeen imposed on the satellite by an active source suchas a laser or lamp. A retroreflector is an optical prismwith the property that an incident ray is reflectedback on itself over a moderate range of incidenceangles. Thus, when irradiated by a laser beam firedfrom the ground, a retroreflector acts like a highlydirectional source pointed directly back at the site. Aslong as the retroreflector is small enough so that itacts like a point source, atmospheric aberrations expe­rienced on the uplink leg do not appear on the phasefront of the return beam, and the wavefront receivedat the adaptive optics system has only the downlinkaberrations imposed on it.

The angular acceptance of a large retroreflector isabout 30° full width at half maximum, so a singleretroreflector could be used as a beacon only ifpointedat the ground site to within ±I5°. Because the LACEsatellite is nadir-pointing and passively stabilized bygravity, this condition would occur only when thesatellite was nearly overhead. Consequently, the LACE

retroreflector was designed to be an array of small,1-inch-diameter retroreflectors mounted at variousangles to provide a good return signal for elevationangles from 90° (when the satellite was directlyover the ground site) down to 45°.

The retroreflector array was mounted at the end ofa boom that could be extended to the correct point­ahead distance from the detector array beforeeach pass of the satellite over the ground site (seethe box "Point-Ahead Anisoplanatism"). For an over­head pass, the required boom length was 86 ft; fora low pass with a maximum elevation of onlyabout 50°, the required boom length was about110 ft.

The light source for illuminating the retro-arraybeacon was a CW Ar-ion laser mounted in the beam­director dome. This laser was tuned to a differentwavelength than that of the scoring beam so that itwould not be sensed by the detector array on thesatellite. The beacon laser was transmitted as a small­diameter beam out of the central obstruction of thebeam-director telescope (Figure 13). Because thediameter of the beam was only 2.5 em at thebeam director, diffraction spread the beam to adiameter of about 15 m at the satellite, making itrelatively easy to hit the retroreflector array. In addi­tion, an active pointing system with a band­width of a few hertz made small pointing adjust-

VOLUME 5, NUMBER 1, 1992 THE LINCOLN LABORATORY JOURNAl 39

-MURPHYAtmospheric-Turbulence Compensation Experiments Using Cooperative Beacons

POINT-AHEADANISOPLANATISM

TO BE COMPENSATED effectively,the outgoing laser beam must tra­verse the same column of atmo­sphere measured by the wavefrontsensor. If the laser and beaconpaths do not coincide exactly, theprecorrection that the deformablemirror applies to the laser beamwill not fully cancel out the at­mospheric aberrations actuallyexperienced by the beam, andthe correction will be degraded.Errors resulting from imperfectoverlap of the two atmosphericpaths are known as anisoplanat­ism errors [1].

A common example of thistype of error is angular aniso­planatism, which is caused by rnis­pointing of the scoring laser fromthe beacon path. Angular aniso­planatism can also degrade a com­pensated image if the object be­ing viewed is angularly offset fromthe beacon, in which case the raysthat form the image do not tra­verse the same atmospheric pathas do the beacon rays. This lanerscenario may occur in astronomi­cal applications in which one is

interested in viewing dim objectsin the vicinity of a bright beaconstar.

The amount that aniso­planatism degrades the compen­sation depends on the mismatchbetween the paths and on the tur­bulence conditions. For angularanisoplanatism, the mismatch ischaracterized by the angularpointing error, and the turbulenceis characterized by the isoplanaticangle 80, The definition of 8~ con­tains an integral over the en pro­file similar to that for 70 (see thebox "Derivation of Turbulence­Imposed Requirements for Adap­tive Optics Components"), butwith a range-dependent weight:

L

805/3 = 2. 91k2f z 5/3C;(z)dz.

o

The z5/3 term emphasizes the con­tribution of turbulence at longranges, where the linear separa­tion of the two angularly diver­gent paths is greatest. For point­ing errors less than 80 the beam issaid to be within the isoplanatic

patch and the degradation is mild.The isoplanatic angle at visiblewavelengths for vertical propaga­tion through the atmosphere canvary from a few microradians tomore than 20 ,urad. The relativelysmall value of 80 for visible lightmakes it impractical to apply co­operative-mode adaptive optics toastronomy because only an insig­nificant portion of the sky is cov­ered by (i.e., within an isoplanat­ic patch of) stars bright enoughto serve as beacons.

Angular anisoplanatism is animportant potential error forground-to-satellite adaptive opticsapplications; in that context, it isknown as point-ahead aniso­planatism. The error arises becausehitting a moving target such as asatellite requires the laser beam tobe pointed ahead of the apparenttarget position by the point-aheadangle 8pa =2vl.Ic, where Vl. is thespeed of the satellite perpendicu­lar to the line ofsight, and c is thespeed of light (Figure A). Point­ahead anisoplanatism degrades thecorrection because the scoring

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ments to the laser beam to maximize the return signalfrom the retroreflector.

The detector array comprised 85 discrete Si photo­detectors distributed in a 2-dimensional array (Figure14). To enable the estimation of the total power re­ceived at the satellite, each detector was radiometri­cally calibrated over a range of LO X 10-7 to 5 X 10-3

40 THE LINCOLN LABORATORY JOURNAl VOLUME 5, NUMBER 1, 1992

W/cm2• The wide dynamic range ensured that the

array could measure the beam both with and withoutadaptive optics compensation. The entire array wassampled, or read out, at a I-kHz rate, and the datawere telemetered to the ground for recording andreal-time display. The display allowed the operators totell when the beam was hitting the satellite and to

-MURPHYAtmospheric-Turbulence Compensation Experiments Using Cooperative Beacons

FIGURE A. Point-ahead angle epa of scoring beam fired at a satellite. Thesatellite moves perpendicular to the line of sight with speed v.1 and emits abeacon pulse at time l1' The transmitter on the ground receives the signalafter a transit time of RIc, where c is the speed of light. The system on theground then emits a scoring beam pulse that travels to the satellite andarrives after another transit delay of RIc. By that time, the satellite hasmoved a distance M = 2(Rlc)v.1, so the scoring beam must be pointedahead of the beacon arrival line of sight by epa = MIR = 2v.LIc.

beam must be angularly offset byepa from the atmospheric path ofthe beacon light coming downfrom the satellite. For a satellitein a 500-km orbit, epa is about50 .urad so the scoring beam ispointed well outside the iso­planatic patch and the degrada­tion is severe.

The error caused by point­ahead anisoplanatism can beavoided by positioning the bea­con ahead of the scoring-bearn'saim point by an angle equal toepa' This adjustment wouldallow the scoring beam to befired precisely through the col­umn of atmosphere sampled bythe beacon and still be able to hitthe satellite. Such an approachwas taken in the Low-Pow­er Atmospheric-CompensationExperiment (LACE) in which aleading boom was used to posi­tion the retroreflector the ap­propriate distance ahead of thedetector array (see Figure 13 inthe main text).

Reference1. D.L. Fried, "Anisoplanatism in Adap­

tive Optics," j. Opt. Soc. Am. 72, 52(1982).

R

l = l1 + RIc

Scoring Beam fromAdaptive Optics

Beacon Lig'lt toAdaptive OptiCS

............ .. -,.oo .... _......... ,._..: I

: 1-' ..~-~ ~: ~"~ .. ' .. ~_ ........ _ .... I

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judge the effectiveness of the compensation. The real­time data were also used to drive a very-low-band­width pointing loop that kept the scoring beam cen­tered on the array, thereby making the most efficientuse of the relatively dense detector spacing at thecenter of the array.

Satellites with high slew rates impose an additionaltemporal bandwidth requirement on the adaptive op-

tics system beyond the requirements for star compen­sation. As far as adaptive optics applications are con­cerned, wind is the dominant factor that determinesthe dynamics of atmospheric turbulence. It is as­sumed that the turbulence aberrations are "frozen"in layers in the atmosphere, and that each layer issimply blown across the beam. The wind may beeither the natural wind blowing across the beam or

VOLUME 5, NUMBER 1, 1992 THE LINCOLN lABORATORY JOURNAL 41

-MURPHYAtmosphmc-Turbuknu Compmsation Expmments Using Coop"ative Beacons

100010-6 l.__--l_.L.-.L-l.~..w...l.__---JL.._..L_.I._l....L.J...L..L.l.___l.__..L_.I._l....L.J..J..l.J

1 10 100Frequency (Hz)

FIGURE 15. Open-loop power spectral densities (PSD) of single-axistilt fluctuations measured from the satellite retroreflector beacon andfrom a star. Note the increased high-frequency power in the satellitespectrum.

102

NI-"""tJ«l 10...{l2,Cl(j)a..~ 10-2i=~-::JEN 10-4<{

the pseudowind generated by sweeping the beamthrough the atmosphere. For a slew rate of 10 mrad/sec, which is appropriate for the LACE satellite, thepseudowind speed at a range of 5 km, for example,is 50 m/sec--quite a bit higher than the speed ofnatural winds.

The effect of the high slew rate can be readilyobserved in the spectrum of the tilt fluctuationsmeasured by the tracker with the tilt compensationloops open. Spectra measured on different nightswith a star beacon and the LACE retroreflector bea­con are plotted in Figure 15. Because the turbu-

LACE Data - November 30, 1990 LACE Data - November 30, 1990

1 •

uncompensated Compensated

(a) (b)

FIGURE 16. SWAT atmospheric-compensation experimental results: (a) uncompensated and (b) compensatedscoring beam profiles measured at the LACE satellite. The elevation was 85°, and '0 was about 9 em.

42 THE LINCOLN LABORATORY JOURNAL VOLUME 5, NUMBER 1, 1992

-MURPHYAtmospheric-Turbulence Compensation Experiments Using Cooperative Beacons

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,

lence was somewhat stronger on the night the satel­lite tracking data were recorded, the overall spectrumfor the satellite is higher than that for the star. Never­theless, it is easy to see a disproportionate increasein tilt at high frequencies for the satellite beacon.For this reason, the tracking system was designed forclosed-loop operation with a bandwidth of 600 Hz.Similar considerations apply for the figure-compen­sation loops.

Compensation experiments were performed withthe LACE satellite over a 14-month period that beganshortly after launch of the satellite (February 1990)and ended at the conclusion of the SWAT program(April 1991). Nighttime passes that were visible fromAMOS and that had an elevation of at least 45° werecandidates for tests. On average, there were about 20such passes per month, although not all were sched­uled for SWAT experiments. The duration of a passfrom an elevation of45° ascending to 45° descendingwas 2 to 2t min.

The quantitative results of the satellite tests cannotbe presented in this article, bur Figure 16, whichshows open- and closed-loop scoring-beam profilesmeasured at the satellite, at least gives a qualitativedemonstration of the scoring-beam compensation.The profiles are plotted so that each vertex in the gridcorresponds to a detector in the array on the satellite.The profiles appear a little coarse because of the rela­tively sparse sampling performed at the satellite. Nev­ertheless, it is easy to see the concentration of beamenergy that occurred when the compensation wasapplied.

Conclusion

The ability of adaptive optics systems to compensatefor atmospheric turbulence by using cooperative bea­cons is by now well established. Previous experimentsperformed as part of Lincoln Laboratory's Atmo­spheric-Compensation Experiment (ACE) demon­strated propagation of a low-power laser beam to anaircraft and to sounding rockets. The ACE resultshave been complemented by the recent Shoft­Wavelength Adaptive Techniques (SWAT) tests,

which demonstrated high-bandwidth tracking andnear-diffraction-limited compensated imaging ofstars, as well as propagation of a compensated laserbeam to a low-orbit satellite having a high slewrate. Taken together, these experiments provide agood base of experimental data for a variety ofapplications and a wide range of atmosphericconditions.

Acknowledgments

The design, development, and operation of the SWATadaptive optics system required the work of manypeople at Lincoln Laboratory. In particular, RobertKramer was the original system engineer; AldenMarshall, Pete Rossini, Pete Smith, and Irv Wigdordeveloped the tracking system; Bert Willard designedthe opticallayour; Jim Mooney designed the wavefrontreconstructor; Jon Twichell and Herb Barclay devel­oped the wavefront sensor; Brian Player and GregRowe developed the display for the LACE data;Jan Herrmann, Ron Parenti, and Rich Sasiela pro­vided the theoretical analysis; and Dan Pageand Byron Zollars assisted in conducting theexperiments.

This work was supported by the Strategic DefenseInitiative Organization.

REFERENCES

1. B.G. Zollars, "Atmospheric-Turbulence Compensation Ex­periments Using Syntheric Beacons," in this issue.

2. J.W. Hardy, "Adaptive Optics-A Progress Review," Proc.SPJE 1542,2 (1991).

3. J.e. Twichell, B.E. Burke, RK. Reich, W.H. McGonagle,e.M. Huang, M.W. Bautz, J.P. Doty, G.R Ricker, RW.Mounrain, and V.S. Dolat, "Advanced CCD Imager Tech­nology for Use from 1 to 10000 A," Rev. Sci. [nstr. 61, 2744(1990).

4. HT. Barclay, P.H. Malyak, W.H. McGonagle, R.K. Reich,G.S. Rowe, and J.e. Twichell, "The SWAT Wavefront Sen­sor," in this issue.

5. J. Herrmann, "Least-Squares Wave Front Errors of MinimumNorm," J Opt. Soc. Am. 70, 28 (1980).

6. RJ. Sasiela andJ.G. Mooney, "An Optical Phase Reconstruc­tor Based on Using a Multiplier-Accumulator Approach," Proc.SPJE 551,170 (1985).

VOLUME 5. NUMBER 1. 1992 THE LINCOLN LABORATORY JOURNH 43

-MURPHYAtmospheric-Turbulence Compensation Experiments Using Cooperative Beacons

DANIEL V. MURPHY

received a BA. degree in phys­ics from Amherst College and aPhD. degree in engineeringand applied science from YaleUniversiry. Dan is a staff mem­ber in the High-Energy-LaserBeam Control and PropagationGroup, where his focus ofresearch has been in adaptiveoptics.

44 THE LINCOLN LABORATORY JOURNAL VOLUME S, NUMBER 1. 1992

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